Most colleges have to take a certain percentage of incoming students from their own program, and a certain percentage from other programs coming in. My guess is there is room for several students who have done their undergrad at that particular institution, but because KSU is a good school and a large school, there might be some competition for those spots. I'm not sure the best advice to have your daughter take a dive on her undergrad work just so she doesn't have to compete for those coveted spots against other good students. I would recommend you talk to somebody from the vet school and find out more about that, and see if they can recommend some other undergrad programs that would have her well-prepared for the KSU vet school requirements.
I just visited Kansas State for a large conference, and I've known several people who have graduated from there. I was EXTREMELY impressed with the ag department there, and particularly the animal science department, and if I were starting over, I doubt there would be any other school in the country I would rather go. It's one of the few ag programs that is growing and committed to the study of traditional animal sciences, rather than cutting the budget every year, adjusting the curriculum to get non-ag kids to enroll, and still having less students come into the program.
Way back when I was in school, Oklahoma State, Auburn and Tennessee all had good animal science programs and very strong vet schools. I'm sure there are a few more, but when you're considering the top vet schools, the list gets shorter. And the list for strong animal science programs is also getting shorter and shorter nowadays! One speaker from KSU estimated that within a few years, there would be about five animal science programs in the country that were continuing to grow and continuing to increase their budgets instead of cutting back. It's definitely worth taking a look at, and if she's serious about it and you're serious about sending her there, I would recommend you make the trip to Manhattan and take a look around. You'll be impressed.